Quantum mechanical systems have been investigated for many applications including quantum cryptography and quantum computation. Information may be stored and processed in such a quantum system. Often the information is carried by two-state quantum subsystems. Each two-state quantum subsystem is called a quantum bit (qubit).
Quantum bit can be applied to quantum computers. The quantum mechanical state of a physical system represents the logical state of the computers. Such a computer is called a “quantum computer” and the logical gates in such a computer are called “qubits”. A quantum computer would be able to solve certain types of problems far more rapidly than any conceivable classical computer. For example, such tasks as searching, encryption, and searching a large database for the optimal solution to a multidimensional optimization problem would be orders of magnitude faster on a quantum computer.
The reason for this drastic increase in capability is the following. In an ordinary classical computer, the logical state of the computer is represented by “0”s and “1”s, or in other words, the classical states of a physical system. Therefore, the basic logic gate in the classical computer stores a single bit of information. In contrast, a qubit simultaneously stores multiple bits of information.
At the center of quantum computing realization is the physical implementation of qubits, two-state quantum information units. The rise of graphene has opened a new door to the implementation. Because graphene electrons simulate two-dimensional relativistic particles with two degenerate and independent energy valleys, a novel degree of freedom (d.o.f.), namely, the valley state of an electron, emerges as a new information carrier.
A fundamental issue of physical implementation of qubits is that a quantum system with information carriers suffers from environment-caused fluctuation and the encoded quantum information may be lost in the environment due to decoherence. In addition, following the example of conventional microelectronics, one would like to manipulate qubits with purely electrical means, as well as fabricate scalable and fault-tolerant circuits for quantum computing. To sum up, a qubit implementation faces three important issues, namely, i) all electrical manipulation, ii) state relaxation/decoherence, and iii) scalability and fault tolerance. In the spin qubit case (where the logic 0/1 states are represented by the spin “up or down” states), the paradigm quantum dot (QD) approach (using confined electron spins) usually serves as the foundation (referred to: D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A. 57, 120 (1998); G Burkard, D. Loss, and D. P. DiVincenzo, Coupled quantum dots as quantum gates, Phys. Rev. B 59, 2070 (1999).), upon which one applies the additional tactics including: utilization of the Rashba mechanism of spin-orbit interaction (SOI) to achieve i), materials with weak SOI and vanishing hyperfine field (HF), e.g., graphene or carbon nanotube (CNT), to resolve ii), and spin singlet-triplet qubits to iii).
Being solutions to separate issues, these tactics are sometimes at odds with one another, in a material-dependent way. For instance, in materials with strong Rashba SOI, HF or SOI inevitably cause state mixing (referred to: A. V. Khaetskii and Y. V. Nazarov, Spin relaxation in semiconductor quantum dots, Phys. Rev. B 61, 12639 (2000).; T. Meunier et al., Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot, Phys. Rev. Lett. 98, 126601 (2007).; A. Pfund et al., Spin-state mixing in InAs double quantum dots, Phys. Rev. B. 76, 161308, (2007).). For this reason, varied materials, e.g., GaAs (referred to: J. Pella et al., Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309, 2180 (2005).; F. H. L. Koppens et al., Driven coherent oscillations of a single electron spin in a quantum dot, Nature 442, 766 (2006).; K. C. Nowack et al., Coherent control of a single electron spin with electric fields, Science 318, 1430 (2007).), CNT (referred to: H. Ingerslev et al., Singlet-triplet physics and shell filling in carbon nanotube double quantum dots, Nature Phys. 4, 536 (2008).), or InAs (referred to: S. Nadj-Perge et al., Spin-orbit qubit in a semiconductor nanowire, Nature 468, 1084 (2010).), have been exploited, in the recent experimental breakthroughs in spin qubit demonstration.
As mentioned above, in prior research and development of qubits, the utilization of certain semiconductor materials or CNT may overcome some of the issues that spin qubits are facing. However, such solutions are incomplete. Take CNT for example, because of weak SOI and HF in CNT, electron spin qubits in this material can have long coherence time. However, the weak strength of SOI in CNT also makes it hard to manipulate spin qubits by electrical means.
The present invention provides a carbon-based qubit device, namely, the graphene valley singlet-triplet qubit that can improve in all of the issues in spin qubits (i-iii in [0006]) and the three corresponding tactics resolving these issues can be fully realized (in their “valley” version) without conflict with one another.